Implement more types of measurable elemwise transformations

[ricardoV94]

We already have support for

• add (and subtraction via addition)
• mul (and division and neg via multiplication)
• pow (inludes reciprocal, sqrt, sqr, etc...)
• exp
• log
• abs

Other operations we could support

• cosh, sinh and tanh (maybe other?)
• erf, erfc, erfcx?
• arcsinh, arctanh (see https://discourse.pymc.io/t/the-sinh-arcsinh-normal-distribution/12136)
• arccosh is multivalued, or complex? Didn't have time to dig

pymc/pymc/logprob/transforms.py

Line 339 in f3ce16f

valid_scalar_types = (Exp, Log, Add, Mul, Pow, Abs)

Other operations we can support via rewrites to already supported forms

• exp2, log2, log10
• log1p
• expm1
• log1mexp
• log1pexp (softplus)
• sigmoid

Example of such rewrites:

pymc/pymc/logprob/transforms.py

Lines 467 to 483 in f3ce16f

	@node_rewriter([neg])
	def measurable_neg_to_product(fgraph, node):
	"""Convert negation of `MeasurableVariable`s to product with `-1`."""
	inp = node.inputs[0]
	if not (inp.owner and isinstance(inp.owner.op, MeasurableVariable)):
	return None
	rv_map_feature: Optional[PreserveRVMappings] = getattr(fgraph, "preserve_rv_mappings", None)
	if rv_map_feature is None:
	return None # pragma: no cover
	# Only apply this rewrite if the variable is unvalued
	if inp in rv_map_feature.rv_values:
	return None # pragma: no cover
	return [pt.mul(inp, -1.0)]

[LukeLB]

@ricardoV94 is this just a continuation of the work done here https://github.com/pymc-devs/pymc/pull/6414/files? If so I can follow what I did there and knock a few of these off

[ricardoV94]

Yes, 👍

[LukeLB]

I've created Transform classes for cosh, sinh, tanh, erf, erfc however there doesn't appear to be an inverse function available for erfcx in pytensor or pymc.math. Any suggestions on what to do here? It feels like writing a new function in pytensor for erfcxinv may be overkill for this issue...

[ricardoV94]

You can exploit the equivalence between erfcx and erfc https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.erfcx.html

So you don't need a specific transform, just to rewrite it into that form.

[LukeLB]

So if I rewrite it into that form I can get the foward function, but I don't understand how to get the backward function from that? This discussion on the inverse of erfcx in Matlab seems to suggest writing a specific functon https://www.mathworks.com/matlabcentral/answers/302915-inverse-of-erfcx-scaled-complementary-error-function

[ricardoV94]

@LukeLB my bad, I didn't notice that x shows in both terms (of course it does). So the forward form can't be easily inverted as you said.

Writing a specific function seems like a nice (but perhaps low impact) challenge. Up to you if you want to pursue it ;)

[LukeLB]

Not to worry, it did have me confused for a bit there!

This is all a learning experience for me so happy to add value (even if small) wherever I can. What do you reccomend I do?

Presumably open a new issue in PyTensor and link to this issue? Or can I just directly put in a PR on PyTensor for the function?

[ricardoV94]

I think you can implement it directly in pymc using Scan and Switch statements as building blocks.

[ricardoV94]

@LukeLB any interest in picking some of the new ones I added: arcsinh and arctanh?

A user on discourse was asking how to implement the sinh-arcsinh normal distribution: https://discourse.pymc.io/t/the-sinh-arcsinh-normal-distribution/12136

The only ingredient missing is the arcsinh I think

[LukeLB]

@ricardoV94 really sorry I seem to have messed up by notifications when switching email addresses and didn't get an email through for this. Yes, I'd be interested in implementing these additional transformations! I'll have a look this week.